Why do interest rates change?
Interest is simply the cost of borrowing money. As with any good or service in a free market economy, price ultimately boils down to supply and demand. When demand is weak, lenders charge less to part with their cash; when demand is strong, they're able to boost the fee, aka the interest rate. Demand for financing ebbs and flows with the business cycle. During a recession, fewer people are looking for new mortgages or loans to start up or extend businesses. Eager to increase lending, banks put their money "on sale" by dropping the rate.
Supply also changes as economic conditions fluctuate. In this regard, the government plays a major role. Central banks like the United States Federal Reserve tend to buy government debt during a downturn, pumping the stagnant economy with cash that can be used for new loans. The increase in supply, combined with diminished demand, forces rates downward. The exact opposite occurs during an economic boom.
It's important to note that short-term loans and long-term loans can be affected by very different factors. For instance, the buying and selling of securities by a central bank has a much greater impact on near-term lending, such as credit card rates and car loans. For lengthier notes, such as a 30-year Treasury bond, the prospects for inflation can be an important factor. If consumers fear the value of their money will rapidly decline, they'll demand a higher rate on their "loan" to the government. (For related reading, see Why do interest rates tend to have an inverse relationship with bond prices?)